The fractional memory of non-Hermitian systems

Recent years have marked a paradigm shift in physics research, as systems described by non-Hermitian (NH) Hamiltonians have attracted vastly increased attention.

In the quantum regime, NH descriptions become relevant when a system is allowed to interact with its environment, and in the case it comprise a memoryless, or Markovian, bath, their dynamics are understood via, e.g., the Lindblad formalism.

The proposed project aims to go beyond the Markovian picture, and provide an understanding of non-Markovian (NM) bath dynamics, its connection to topology, and its physical consequences in terms of NH phenomena.

Understanding such systems in all its generality is immensely complicated, which is why a recent and alternative method including fractional derivatives, a generalization of the concept of derivative that recently has proven to be connected to NM effects, will be applied.

The project will partly focus on investigating NM extensions of well-studied Markovian models to unravel concrete differences, and partly treat the question fundamentally in an attempt to derive the general form of NH operators admitting a description in terms of an open NM system.

The theoretical predictions will be complemented by experimental collaborations to provide platforms where they can be probed.

In this way, this new research branch will increase the fundamental understanding of open quantum systems, a necessary step to pave the way towards modern applications in future tech devices.